Use examples to justify your response to each of the following questions: How can a rational function switch between positive and negative intervals without an x-intercept? . Why is this an important factor to think about when solving an inequality? • How would the intervals of the solution set differ between a polynomial inequality and a rational inequality?

Q: Identify the solution set in the given rational inequality. x² - 8x + 15 x² - 2x + 1 ≥ 1

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Q: Which boundary points must I always exclude from the solution set of a rational inequality?

A: Consider the given information.   As the given information, those boundary points must always…

Q: Given f(x) = 2x3 − 5x2 − 28x + 15, a.Find all the zeros of f(x) b. Identify the x-intercepts of the…

A: “Hey, since there are multiple subparts , we will answer the first three subparts alone. If you want…

Q: Solve the rational inequality. Express your solution set in interval notation. x+2 Type your…

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Q: Identify the solution set in the given rational inequality. x-1 x - 10 S x² - 2x + 1 x² - 100

A: We know that: a2-b2=a+ba-ba2-2ab+b2=a-b2

Q: ny fixed number n representing the perimeter of a rectangle, what are the dimensions of ectangle…

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Q: a. Can a quadratic function have a range of (- ∞, 0)? Justify your answer. b. Discuss the…

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Q: Identify the solution set in the given rational inequality. x + 4 x²16 <0

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Q: Find the solution set of this rational inequality 1. x + 3 + 1 > 0       x   Write TRUE if the…

A: First we simplyfy the given equation and find it's solution set. Then check  x=9 , x=-5 is a…

Q: 6. Solve the following quadratic inequality by sketching the graph of the corresponding quadratic…

A: from given information, f(x) = -(x-3)2 this equation is true for -x2+6x-9 &lt; 0

Q: Answer the following questions: 1. Why are rational functions important? 2. How can rational…

A: 1)A rational function is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are…

Q: True or False The graph of f(x) = is above the x-axis X - 3 for x 3, so the solution set of the…

A: Given: fx=xx-3 is above x-axis for x&lt;0 or x&gt;0 To check whether the statement, 'The graph of…

Q: n 4 3 La S T 3 y 2 3 4 Move the 3 points to graph a quadratic function f(x) so the inequality f(x) >…

A: A graph of the parabolic function. To Find:  Move a three-point to graph the quadratic function so…

Q: 1. Based on the graph of a function, how can you tell what degree a function is? 2. Explain the…

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Q: 1. a) What is the difference between the reciprocal functions of a linear equation and a quadratic…

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning : "I…

A: x+1x+3≥2 First we must make the value of right hand side as zero. For this we need to subtract 2 on…

Q: Q6. Use the graph of the quadratic function sho 5 5. to solve the inequality y > 0 1 5 1 > x > 5 1…

A: Observe the graph and select the values of x for which curve is above the x - Axis.

Q: Identify the solution set in the given rational inequality. x-1 x - 10 x² - 2x + 1 x² 100

A: (x-1)/(x-10) &lt;=(x2-2x+1)/(x2-100).

Q: For inequality (x-2/x-3 <= 2x+5/9x-7), if we were to draw an interval chart, what would it look…

A: the answer is in step 2.

Q: Your friend looks at the inequality (1 + 1/x) &gt; 2 and, without any computation, states that the…

A: Given: The inequality (1 + 1/x) &gt; 2 , the solution set of all real number between 0and 1.

Q: 1. Determine an equation for the graph of the polynomial function shown. ✓✓ -2 2 2. Determine…

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Q: 1a) Sketch the graph of f(x) = -2 (x+1)^3 (x-2)^2 using zeros, y-intercept, and end behaviour. Label…

A: Note: As per the guidelines we are supposed answer only 3 subparts of a question. Please repost for…

Q: Use the graph of the rational function to solve the inequality: 1/4(x + 2) ≤ -3/4(x - 2)

A: Given: 14x+2≤-34x-2 for finding solution of given inequality by using graph method, we draw graph of…

Q: I am having trouble understanding solving inequalities. I know that I have to set the numerator and…

A: To obtain the solution of the given inequality in interval notation, find the signs of the factors…

Q: Set up and algebraically solve a quadratic inequality that results in the domain of each of the…

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Q: Solve the following rational inequality: 23/44 x-4 x+6 Solve by making a detailed sketch of the…

A: Given: xx+6≥3x-4 To Find: Solve the above inequality and also sketch the graph using a table of…

Q: Discuss the possibilities for the number of times the graphs of two different quadratic functions…

A: Answer is mentioned below

Q: resolves the following inequalities and represents its solution graphically. -3 + 2x - 6 ≥ 0

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